Measuring With Shadows

Did you know that you can use shadows and a meter stick to measure very tall objects from the ground? You can measure a tall building or a tall tree. If you could travel back in time, you could even measure the height of a Tyrannosaurus Rex. Let us do that!

Click and drag the slider to change the time of the day. Notice how the relative position of the sun and the length of the shadows change during the day. Also, notice the change in the division formula. Dividing the length of the T-Rex's shadow by the length of shadow of the meter stick gives us the height of the T-Rex.

All you have to do is to stand the meter stick upright. Look at the shadow that it casts on the ground. Mark the length of the shadow then measure its length. Now comes the tricky part. Very carefully approach the T-Rex. Remember a T-Rex is carnivorous, and would love to have you for a snack. Measure the length of the shadow of the T-Rex.

The lengths of shadows cast by the same light source are always proportional. For example, if the shadow of the meter stick is twice as long as its height, then the shadow of the T-Rex will also be twice as long as the T-Rex's height. Notice that this is true at 6:10 a.m. At this time, the shadow of the meter stick is 2 meters long. The shadow of the T-Rex is 12 meters long. If we divide the length of T-Rex's shadow by the length of the shadow of the meter stick, we get the height of the T-Rex: 6 meters! Try it at different times. Be careful. You may be making the T-Rex nervous.